This paper describes the coupling effect between transient magnetic fields with structural vibrations of shallow arches and a thin plate with a crack. A thin electrically conducting plate and an arch are used as the structural components of a fusion reactor. When an impulsive magnetic field due to plasma disruption acts on these thin structures, the induced current produces electromagnetic forces by its interaction with the very strong magnetic field. They are acted on by an impulsive electromagnetic force, which causes them to vibrate and sometimes show magnetoelastically unstable behavior. When an additional current arising from the movement of a vibrating structure is induced under an external magnetic field, the Lorentz force sometimes acts as a damping force and makes the deflection smaller. This force can be evaluated if the coupling effect between the eddy current and the deflection is considered. Hence it is very important to evaluate the dynamic behavior caused by this coupling effect. A computer code to calculate the eddy current and deflection has been developed that takes this effect into consideration. The code was applied to the dynamic response analysis of shallow arches. The critical current or field that causes a large deformation for small increment in current (a kind of snap-through instability) was evaluated. It was also applied to the dynamic deflection of a plate with a crack. The coupling effect was evaluated in these problems. The effective use of the coupling effect might decrease the maximum stress of thin structures during the disruption.